Desktop application for static analysis of a straight beam and stress evaluation across the cross-section. Built for structural / strength engineering work: internal forces, deflection, accurate section properties and reserve-factor assessment.
Python · PySide6 · NumPy · Matplotlib · SciPy.
Current release: 1.41.
⚠️ This repository is read-only. Issues are welcome, but external pull requests are not accepted at this time.
BEAMER is an engineering aid and learning tool, not a certified design tool. It is provided as is, without any warranty (see LICENSE). Results may contain errors. Always verify any result with an independent method before using it in design, analysis or certification. The author accepts no responsibility for decisions made on the basis of its output.
- Beam solver — direct stiffness method with the backward-compatible 6-DOF Saint-Venant model and an optional 7th warping DOF for Vlasov torsion. Handles statically indeterminate beams; choice of Euler–Bernoulli or Timoshenko theory. The mesh is refined automatically for accurate deflection.
- Biaxial bending — loads in both transverse planes (vertical Fz and horizontal Fy, or a force at any angle around the beam), with skew-bending coupling through the product of inertia Iyz for unsymmetric/rotated sections. A purely vertical (planar) problem behaves exactly as before.
- Internal forces & deformations — axial force N, shears V_z/V_y, bending moments M_y/M_z, torsion Mk, Saint-Venant/warping torque, bimoment, twist and deflections w/v along the beam, with extrema marked.
- Segment-based model — the beam is built from segments; each segment has its own length, material (from the library) and cross-section (including tapered transitions). The solver uses per-segment E, G and material strengths (Re, Rm).
- Cross-section library — rectangle, hollow rectangle (RHS), circle, tube (CHS), I, T, L, U/C, an arbitrary polygonal section, and a direct section defined by its properties A, Iy, Iz, IT (for tabulated profiles).
- Composite (multi-body) sections — a section may contain several separate bodies, each with its own outline and any number of holes. The whole assembly is evaluated as one section (composite A, Iy, Iz, IT).
- Accurate section properties — area A and moments Iy, Iz, Iyz from the exact Green's-theorem integration; torsion constant IT, warping constant Iω, shear-center location and effective shear areas from a finite-element Saint-Venant solver (quadratic T6 triangles). Principal moments, radii of gyration, section moduli and plastic moduli are reported as well.
- Stress & assessment — normal and shear stress, von Mises equivalent stress, and the reserve factor (RF) against yield and ultimate strength along the entire beam (RF ≥ 1 means the section passes). An optional exact 2D FEM shear field is available in addition to the legacy shear model.
- Supports & loads — pin / roller (at an angle) / fixed, plus elastic springs and, for rigid supports, a clearance (unilateral contact) or a prescribed settlement. Point forces, moments, torsion, distributed loads (including from a pasted x, q curve) and thermal loads — uniform ΔT (axial) and a through-depth gradient (thermal curvature / bending).
- Load combinations & envelope — an envelope of internal forces and RF across all combinations, plus a conservative hand-analysis-style check.
- Column buckling — a per-segment Johnson–Euler check (weak axis, editable buckling-length factor μ) and a system eigenvalue buckling analysis (phase 2): the critical load factor and mode shape from the geometric stiffness matrix, with the effective length following from the boundary conditions.
- Local stability — elastic plate buckling and Needham/Gerard crippling for parameterized I/T/L/U/box thin-walled sections with explicit wall topology.
- Material library — common aerospace alloys and steel; custom materials with arbitrary E, G, ν, Re, Rm, ρ.
- Files & export — human-readable JSON projects; polygon import from text coordinates and a planar IGES/IGS subset; text and DOCX reports; PNG export of diagrams.
- Bilingual UI — English / Czech (switchable in Settings).
Requires Python 3.11+.
pip install -r requirements.txtDependencies: PySide6, NumPy, Matplotlib, SciPy.
SciPy is required for the exact FEM torsion / warping properties of arbitrary (polygonal) sections. Without it, those properties fall back to approximate estimates.
python main.pyOn Windows you can also use BEAMER.bat, which launches the app without a
console window.
To package BEAMER into a single standalone .exe, see
BUILD_EXECUTABLE.md.
A full user manual is available: manual/BEAMER_manual_EN_v1.41.docx.
A verification suite checks the results against closed-form solutions (cantilever / simply supported / fixed-fixed beams, torsion, Timoshenko vs Euler–Bernoulli, stress sign convention):
pip install -r requirements-dev.txt
python -m pytest beamer/tests/ -vThe beam is solved as a planar frame element by the direct stiffness method and discretized at supports, hinges, loads and segment boundaries. Section properties combine an exact Green's-theorem evaluation of A, Iy, Iz, Iyz with a FEM Saint-Venant solution for torsion, warping, shear center and shear areas. Stress is assembled from the internal-force contributions (σ = N/A + M·z/Iy, τ = V·Q/(Iy·b) + Mk·t/IT, …) and reduced by the von Mises criterion; the reserve factor is RF = min(Re, Rm)/σ_red.
Section properties are checked against closed-form analytical values. Area and moments of inertia (A, Iy, Iz, Iyz) come from exact Green's-theorem integration and match analytical results to machine precision; torsion, warping and shear-center quantities come from the FEM solver and show the small mesh-dependent deviations expected of a discretized solution.
| Case | Quantity | Analytical | BEAMER |
|---|---|---|---|
| Rectangle 100 × 60 mm | A | 6 000 mm² | 6 000 |
| Iy = b·h³/12 | 1 800 000 mm⁴ | 1 800 000 | |
| Iz = h·b³/12 | 5 000 000 mm⁴ | 5 000 000 | |
| Square 100 × 100 mm, centered 40 × 40 hole | A | 8 400 mm² | 8 400 |
| Iy = Iz = (100⁴ − 40⁴)/12 | 8 120 000 mm⁴ | 8 120 000 | |
| Composite: two 100 × 20 flanges at z = ±90 mm | A | 4 000 mm² | 4 000 |
| Iy = 2·(b·t³/12 + A·d²) | 32 533 333 mm⁴ | 32 533 333 | |
| centroid / shear center | (0, 0) | (0, 0) |
The FEM Saint-Venant core (torsion constant J/IT, warping constant Iω, shear center, shear areas) follows the formulation in W. D. Pilkey, Analysis and Design of Elastic Beams (Wiley, 2002), and was cross-checked against reference section-property tools.
This is a starting set, not exhaustive coverage. If you find a case where the output disagrees with a trusted reference, please open an issue.
Licensed under the Apache License 2.0 — see LICENSE. Copyright © 2026 mrSpringpeace.